Consistent stoichiometric long-term relationships between nutrients and chlorophyll-a across shallow lakes

Aquatic ecosystems are threatened by eutrophication from nutrient pollution. In lakes, eutrophication causes a plethora of deleterious effects, such as harmful algal blooms, fish kills and increased methane emissions. However, lake-specific responses to nutrient changes are highly variable, complicating eutrophication management. These lake-specific responses could result from short-term stochastic drivers overshadowing lake-independent, long-term relationships between phytoplankton and nutrients. Here, we show that strong stoichiometric long-term relationships exist between nutrients and chlorophyll a (Chla) for 5-year simple moving averages (SMA, median R² = 0.87) along a gradient of total nitrogen to total phosphorus (TN:TP) ratios. These stoichiometric relationships are consistent across 159 shallow lakes (defined as average depth < 6 m) from a cross-continental, open-access database. We calculate 5-year SMA residuals to assess short-term variability and find substantial short-term Chla variation which is weakly related to nutrient concentrations (median R² = 0.12). With shallow lakes representing 89% of the world’s lakes, the identified stoichiometric long-term relationships can globally improve quantitative nutrient management in both lakes and their catchments through a nutrient-ratio-based strategy.

While the underlying approach and hypotheses are intuitive, my biggest critique of the paper is that the execution of the statistical approach used was more difficult to comprehend (as likely evidenced by the long Supplementary Information file), and this may limit the readership or citations of this paper.After fully reading the Supplementary Information file, the approach used made more sense to me, but this wasn't apparent on initial reading of the paper.
Below, I provide general and mostly specific comments to help improve the overall quality of the manuscript.
General comments: 1.The modeling approach used in this paper requires a very detailed description in the Supplementary Information, including a lengthy section describing simulations to demonstrate that the Simple Moving Average (SMA) approach can successfully decompose trends from short-term noise (variation; see Section 4).The Supplementary Information also contains justifications for the selection of the appropriate SMA model and regression model.While I think that the information was helpful, the lengthy descriptions also demonstrated that the approach is rather complex and not intuitive.I realize that this is a short format paper, but it might be helpful to re-evaluate if some of the information in the Supplementary Information should be in the main text.2. I think that the structure of the manuscript could be streamlined a bit more, largely by removing the sub-headings between presentation of results.For example, the description of longterm results using 5-year SMAs (lines 87-9) is very general, and does not describe the relationships between chlorophyll and total phosphorus or total nitrogen, including whether or not these support hypotheses (yes for phosphorus, no for nitrogen).These results are not described until the following two sections (lines 146-51 for phosphorus; lines 155-9 for nitrogen).The same applies to results for the residuals (lines 89-90).3. The only criterion used for including data in analyses was that the lakes were < 6 m depth, which was used to focus on shallow, polymictic lakes (lines 248-50).I believe that there were likely still thermally-stratified lakes included in the dataset, which begs the question of why was the entire dataset not used?Would the 10% of observations that came from deeper lakes be enough to mask relationships?I don't believe that previous studies exploring empirical relationships between chlorophyll and nutrients have excluded deeper lakes, which confounds comparisons.4. The commentary regarding alternative pathways for N fate in high TN:TP lakes (lines 184-91) seems a little speculative.This was presented as a hypothesis, but it seemed like there was a lot of discussion regarding it for the short format of this paper.Specific comments: 1. Line 21: Add citation for statement regarding harmful algal blooms (similar to construction for fish kills and methane).2. Lines 31-2: At this point, it is unclear why is this important.Have shallow lakes been underrepresented in the past, or were deeper lakes excluded because they have unique relationships?I think that this should be written as "data from all shallow lakes (here defined as average depth < 6m)..." 3. Line 40: Responses of what exactly? 4. Lines 56-8: Could also include differences in composition, cellular chlorophyll content, and accessory pigments.5. Lines 99-101: I find the reference to the extinction debt model a bit confusing.Recommend deleting.6. Lines 113-16: To me, it is not quite clear how to interpret this comparison.If the HDI for shortterm variation is half that of the HDI for SMAs, does that mean that it is highly variable?It would be helpful to provide some context here.7. Lines 120-1: Why would this just affect short-term variation?What about long-term shifts in phytoplankton communities resulting from eutrophication (e.g., cyanobacteria blooms) or increased cellular chlorophyll quotas due to light limitation?8. Lines 136-8: Do you mean in regards to decomposing short-term fluctuations from long-term trends?There are numerous studies using Mann-Kendall tests to identify long-term trends in water quality parameters despite short-term variability.Please clarify the intended meaning.9. Lines 174-6: Was a regression of nitrate on TN performed?This would give an indication of whether or not nitrate is driving high TN concentrations.Previous work from agricultural regions has shown that nitrate can drive high TN concentrations in lakes (Filstrup and Downing 2017).10.Line 280: Should the window width for TN:TP be 2, not 3? Interval 0.1 seeems really small Lines 281-2.Graeber et al described the relationships between nutrients and chlorophyll-a across lakes with publicly available long-term data.They found that strong relationships consistently existed between nutrients and chlorophyll a for 5-year simple moving averages along a gradient of total nitrogen to total phosphorus ratios.The topic is interesting in general, and the novelty of this study is that the authors applied a big field-observation data to support the thresholds of nitrogen phosphorus deficiency.But this relationship has well reported in previous studies from field and laboratory experiments, and the applied statistical analyses are problematic due to the nonindependence among the used measurements.I am sorry I could not be more positive in this case.I showed my major concerns for this study below.

References
Non-dependence among studied variables prevents further strong statistic supports of the key findings.The authors had very few variables playing around in this study, including Chla, TN, TP, SRP and NO3-N.As the authors stated in the introduction, the measurements of TN and TP and phytoplankton biomass are not independent, and the relationships are often tautologous.This limitation is getting worse when the authors attempted to relate the nutrient-Chla relationships to the TN:TP ratios as the same nutrients were used more than one time.For instance, the relationships shown in Figure 4 are clearly not independent, and for instance, it is the relationship between chla and TP shown in Figure 4D, rather than their ratios between TN.I think the authors were describing the results which could not well supported by their data or statistical analyses.
The study is descriptive in general and lacks in-depth mechanisms behind the findings.The authors applied the data sets to test the thresholds of nutrients, which is consistent in general to previous studies.However, few mechanisms could be revealed from the pure field observations, and the authors provided the potential explanations of chla-TN ratio changes by denitrification and dissolved proteins.I may not agree well these descriptive hypotheses could explain well explain the findings without solid data or experiments.I also do not agree that the authors could provide solid evidence to well explain these findings, which thus leaves the study descriptive in general without inspiring insights behind the well-known topic.
The treatments in statistical analyses are subjective and more explanations or analyses are needed.For instance, why was the 5 years average selected?What are the differences among the averages of different year windows?Why was the depth of 6 meters applied?Did the authors test other water depth thresholds for the generality of the findings?Why were the additive models selected for TN and TP as I am not well persuaded that these two variables could be simply treated in this way?How were the thresholds in TN:TP ratios found?Did the authors applied proper statistical analyses to reveal these thresholds?

General remarks
We thank the reviewers for their insightful comments, which we adress in detail below.All changes in the text are marked by purple color and the respective manuscript lines are mentioned for each change.
We also uploaded a new version of the manuscript and SI markdown files to the online repository.

Reviewer 1 Comment 1 "I think that this is an interesting paper that will be of interest to the readership of Nature Communications, and therefore fits the scope of the journal. Previous research studying empirical relationships between chlorophyll and limiting nutrients has often speculated that breakpoints or thresholds in the relationships (non-linearities) was caused by shifting nutrient limitation, which I think this paper has nicely demonstrated. The sole use of TN:TP ratios to indicate nutrient limitation without considering
nutrient bioavailability is flawed, and this paper improves on that approach.Additionally, analyses are performed on a large dataset of lakes, and I applaud the authors for making their code available.
While the underlying approach and hypotheses are intuitive, my biggest critique of the paper is that the execution of the statistical approach used was more difficult to comprehend (as likely evidenced by the long Supplementary Information file), and this may limit the readership or citations of this paper.
After fully reading the Supplementary Information file, the approach used made more sense to me, but this wasn't apparent on initial reading of the paper."

Reply
We thank the reviewer for this positive comment.We improved readibility by several measures, please see our replies to the comments below.
Comment 2 "1.The modeling approach used in this paper requires a very detailed description in the Supplementary Information, including a lengthy section describing simulations to demonstrate that the Simple Moving Average (SMA) approach can successfully decompose trends from short-term noise (variation; see Section 4).The Supplementary Information also contains justifications for the selection of the appropriate SMA model and regression model.While I think that the information was helpful, the lengthy descriptions also demonstrated that the approach is rather complex and not intuitive.I realize that this is a short format paper, but it might be helpful to re-evaluate if some of the information in the Supplementary Information should be in the main text."

Reply
We are aware that the used statistical approach is non-standard, thus we included a depiction of this approach in Figure 1 in the original submission.We now completely revised the figure caption, shortening and straightening it, by excluding less important information and moving other information to the main text.With that we hope to make our statistical approach easier to understand (see changes in lines 72 -78, line 79, and in caption of Figure 1).
Furthermore, the long SI addresses a lot of aspects of analyses which were supporting the approach of the paper.Here, based also on comment 4 from reviewer, our selection of the length of the running means was not clear.We added a better description of this approach in lines 291 -294 of the revised manuscript.

Comment 3
"2.I think that the structure of the manuscript could be streamlined a bit more, largely by removing the sub-headings between presentation of results.For example, the description of long-term results using 5-year SMAs (lines 87-9) is very general, and does not describe the relationships between chlorophyll and total phosphorus or total nitrogen, including whether or not these support hypotheses (yes for phosphorus, no for nitrogen).These results are not described until the following two sections (lines 146-51 for phosphorus; lines 155-9 for nitrogen).The same applies to results for the residuals (lines 89-90)."

Reply
The first part of the results discussion is dedicated to the differences between short-term and longterm variability and not to the specifics of the links between TN or TP and Chla.To accomodate the comment of the reviewer to improve the flow of the manuscript, we moved the N and P discussion up, and the discussion on short and long-term variability down.We have not marked those changes, as we did not change content, only moved paragraphs around (and because we would have had to color the entire part of the manuscript).Here we also reduced the number of subtitles to improve the reading flow (all changed subtitles have been marked in bold plus purple color).We also shortened the section on N (here all changes have been marked, see also reply to comment on N discussion below, lines 137 -167) to improve the flow.Finally, with that we could also avoid mentioning the same results twice, which further improves the flow.
Comment 4 "3.The only criterion used for including data in analyses was that the lakes were < 6 m depth, which was used to focus on shallow, polymictic lakes (lines 248-50).I believe that there were likely still thermally-stratified lakes included in the dataset, which begs the question of why was the entire dataset not used?Would the 10% of observations that came from deeper lakes be enough to mask relationships?I don't believe that previous studies exploring empirical relationships between chlorophyll and nutrients have excluded deeper lakes, which confounds comparisons."

Reply
We chose 6 m because water samples from lakes with larger average depth have a lower probability to represent the entire water column.Here 1 has shown that 6 m is a critical depth at which the probability of stratification is 0.5.Thus shallower lakes are more likely mixed than stratified.Since we know that the US data from the LAGOS-NE dataset is epilimnetic data, while the Danish data from the Overfladevandsdatabasen integrates the entire water column, removing this depth cut-off would more likely result in comparing different parts of lake water column.Furthermore, we do not know the exact sampling strategy for the remaining data in the global dataset, and using the depth cut-off makes sure that this data can compare well to the other data.This has been described in the Methods section of the original article.We moved some text into the main text and added further information in the Methods to make this clear (lines 97 -99, lines 267 -273).
We now also conduct the same analysis with data from all lakes without depth cutoff and present the results in the SI (SI lines 284 -302).Based on the statistical results, the approach seems highly promising for all lake types, irrespective of lake depth.Specifically the R² patterns change for the highly comparable to the data with depth cut-off.
Still, we keep the depth cut-off, since the dataset is dominated by shallow lakes.Thus, if different patterns would be the case for deeper lakes, we may not be able to see it and, from that deduct false conclusions on deeper lakes.Furthermore, the lower number of deeper lakes precludes us from a separate analysis of those.Finally, one would need to make sure that the water samples also do well represent the entire water column, something which we cannot be certain of, as we already discuss in the previous paragraph.
Comment 5 "4.The commentary regarding alternative pathways for N fate in high TN:TP lakes (lines 184-91) seems a little speculative.This was presented as a hypothesis, but it seemed like there was a lot of discussion regarding it for the short format of this paper."

Reply
We find this discussion important.Some of author team have a biogeochemical perspective and for those co-authors, the potentially overlooked importance of DON for lake N budgets is the most important outcome of the paper.Still we recognize that this part is too long and we feel that is hard to read in parts.Thus we shortened and revised it to make it not stand out too much (lines 148 -167)

Specific comments
1. Line 21: Add citation for statement regarding harmful algal blooms (similar to construction for fish kills and methane).
• Reply: Citation has been added (line 21) 2. Lines 31-2: At this point, it is unclear why is this important.Have shallow lakes been underrepresented in the past, or were deeper lakes excluded because they have unique relationships?I think that this should be written as "data from all shallow lakes (here defined as average depth < 6m)…" • Reply: We agree with the reviewer, and changed the text accordingly (lines 31 -32)

Line 40: Responses of what exactly?
• Reply: We meant variability of responses to changes in TN or TP concentrations at different TN : TP.We corrected that (lines 39 -41).
4. Lines 56-8: Could also include differences in composition, cellular chlorophyll content, and accessory pigments.
• Reply: We agree and argue with this also in the discussion of the results.We now shortly mention this also here (lines 58 -61).
5. Lines 99-101: I find the reference to the extinction debt model a bit confusing.Recommend deleting.
• Reply: Here, the model is an example for a delayed response of a species to a disturbeance.We agree that by itself the mentioning of the model is confusing.We now revise the text to the fact that a disturbance effect (eg. change in nutrient input) may be delayed over long time scales, mimicking the true impact when looking at short time scale data (lines 193 -195) 6. Lines 113-16: To me, it is not quite clear how to interpret this comparison.If the HDI for short-term variation is half that of the HDI for SMAs, does that mean that it is highly variable?
It would be helpful to provide some context here.
• Reply: Well spotted.The reviewer is absolutely correct that the remaining variability is not nearly as high as the one gathered by the long-term data.This was misrepresented in the text.
We revised this to make the difference clearer (lines 203 -205).
7. Lines 120-1: Why would this just affect short-term variation?What about long-term shifts in phytoplankton communities resulting from eutrophication (e.g., cyanobacteria blooms) or increased cellular chlorophyll quotas due to light limitation?
• Reply: We agree that this, in theory, might be important.Yet, statistically, this seems not important in the long-term (here multi-year), as our models do not require any of those factors to explain the Chla response to TN or TP with high R².Specifically, variable Chla quotas would occur due to chanegs in composition or cell-level changes.This would have increased the variability of responses to TN or TP, something which would be visible in the range of uncertainty of R² (the blue scatter around the yellow lines), which we found well constrained (in contrast to the short term R² scatter, Fig. 2).Thus, from our perspective this is more important to discuss for the short-term data.
8. Lines 136-8: Do you mean in regards to decomposing short-term fluctuations from long-term trends?There are numerous studies using Mann-Kendall tests to identify long-term trends in water quality parameters despite short-term variability.Please clarify the intended meaning.
• Reply: Yet, in our opinion, studies fail to see that eutrophication is a long-term process.To our knowledge no study clearly adresses this, and the same we find to be true in ecosystems outside of lakes.This is what this paragraph is about.If the reviewer has specific studies in mind which contrast with our viewpoint, we would be happy to know about them.• Reply: We find that the very high TN concentrations (approx > 3 mg / L) are correlated to very high nitrate-N concentrations, yet up to this range the relationship between TN and nitrate-N is highly variable.We attribute this to the potential importance of DON capturing a lot of the TN (please also see our reply to reviewer comment 5).We now added plots on TN and TP correlations to nitrate-N and SRP at the end of the SI (SI section 11 & 12).Furthermore, we added the reference in the text in the discussion on the links between TN and nitrate-N (lines 142 -143).
• Reply: No the logarithmic TN:TP window width is indeed 3. A step of TN : TP = 0.1 in logarithmic space equals a true change in TN : TP of from eg.TN : TP = 20 to 22.3 but from eg.TN : TP = 100 to TN : TP = 109.Therefore the window moves different lengths in non-logarithmic space.This follows statistic probability density distribution of TN : TP, which is always logarithmic 2 .Here, a larger logarithmic step would move the window much further for higher TN : TP.

Reviewer 2 Comment 1
"Graeber et al described the relationships between nutrients and chlorophyll-a across lakes with publicly available long-term data.They found that strong relationships consistently existed between nutrients and chlorophyll a for 5-year simple moving averages along a gradient of total nitrogen to total phosphorus ratios.The topic is interesting in general, and the novelty of this study is that the authors applied a big field-observation data to support the thresholds of nitrogen phosphorus deficiency.But this relationship has well reported in previous studies from field and laboratory experiments, and the applied statistical analyses are problematic due to the non-independence among the used measurements.
I am sorry I could not be more positive in this case.I showed my major concerns for this study below."

Reply
We thank the reviewer for the comment.We show below in detail that the non-independence is largely not the issue the reviewer proposes.However, the reviewer kindly remarked the non-independence issue in figure 4 which we overlooked.We corrected this.Please see the reply to comment 2 for details.
Furthermore, as also stated in the same reply below, we use non-independence of total nutrients and Chla as a tool, as it only should occur if a nutrient is depleted relative to other nutrients.Please see also details below in the reply to comment 2.
We disagree with the reviewer on the missing novelty on the study.No previous study has reported a global, robust, ubiqituous, stoichiometric deficiency pattern as our study does.Here, the reviewer does not provide literature to support his/ her claim.Hence, we give the most important literature below and compare it to our study: 1. Guildford and Hecky 2000 3 is a kind of standard paper on global stoichiometric thresholds of eutrophication, cited in a multitude of more recent literature, e.g. 4,5.In Guildford and Hecky clearly not independent, and for instance, it is the relationship between chla and TP shown in Figure 4D, rather than their ratios between TN.I think the authors were describing the results which could not well supported by their data or statistical analyses."

Reply
We absolutely agree that in Figure 4, dependence of variables was introduced due to the calculation of ratios between TN and the inorganic nutrient fractions.Hence, we now show absolute concentrations of SRP and nitrate-N in Figure 4.The patterns are like the ones observed for the ratios before.Hence, we come to very similar conclusions on the link between TN : TP and SRP or nitrate-N occurence.We include Chla as color coded variable now, which reveals that for nitrate-N the dichotomous behavior of nitrate-N at high TN : TP persists and is reflected in very different Chla concentrations at this range.In contrast, average Chla concentrations decrease with decreasing SRP with higher TN:TP (> 50) as expected when assuming Redfield ratio (molar N:P = 16) being ideal for phytoplankton growth, and when running into P depletion at higher TN:TP.Please see the new figure 4 The idea of the tautology is actually key to our approach, as we state in the introduction.As originally stated in Lewis (2008) 8 : "Phosphorus and chlorophyll both are essential components of phytoplankton biomass.Therefore, measurements of phosphorus and chlorophyll that are taken in a lake over the same span of time (e.g., the growing season) are not independent variables; there must always be a correlation between the two variables, although the strength of the correlation will weaken if concentrations of phosphorus far exceed the need of phytoplankton for phosphorus." Thus, we agree with the assumption of some correlation, but, more importantly, utilize it for our purpose to assess stoichiometric nutrient depletion of phytoplankton growth.Specifically, the correlation must diminish when the concentration of a nutrient surpasses the requirement for phytoplankton growth.This surpassing can occur either in terms of high concentrations or in terms of a "stoichiometric surpassing", where a different nutrient, rather than the nutrient in question, becomes depleted in concentration.Consequently, the nutrient in question suddenly becomes available in excess, which leads to the weakening of the correlation between this nutrient and Chla.Our concept is strongly supported by the evident systematic correlation patterns observed along the TN:TP gradient, as these patterns strongly indicate such a "stoichiometric surpassing" for long-term averages.

Comment 3
"The study is descriptive in general and lacks in-depth mechanisms behind the findings.The authors applied the data sets to test the thresholds of nutrients, which is consistent in general to previous studies.However, few mechanisms could be revealed from the pure field observations, and the authors provided the potential explanations of chla-TN ratio changes by denitrification and dissolved proteins.
I may not agree well these descriptive hypotheses could explain well explain the findings without solid data or experiments.I also do not agree that the authors could provide solid evidence to well explain these findings, which thus leaves the study descriptive in general without inspiring insights behind the well-known topic."

Reply
The study is strictly empirical, not descriptive, as it uses rigorous statistical testing.We have to improved our explanations to clarify this (see our reply to comment 2 from reviewer 1).Any stoichiometric thresholds that emerge from the statistical analysis are a result of ubiquitously occuring depletion patterns and are not in any way baked into the statistical approach.
In contrast to the notion of the reviewer, we feel that the study will be highly inspiring for further research.It reveals the need to investigate improved stoichiometric management of shallow lakes and their catchments, due to the globally ubiquituous stoichiometric patterns of lake eutrophication, which is crucial for a planet of out of bounds in terms of its nitrogen and phosphorus cycles 9 .Our long-term perspective on eutrophication is unique in contemporary freshwater sciences and proves that long-term patterns in nutrient concentrations are decisive for describing eutrophication, patterns which were expected in the 1980s by some of the most well known ecologists of that time 10,11 .Thus, our study provides unprecedented evidence for the importance of long-term eutrophication research and lake monitoring.It will also be the jump off point for a host of experimental studies testing the proposed mechanisms behind our global data analysis findings, including the proposed refractory DON pool.Please also see our reply to your comment 1 and comment 1 of Reviewer 1 both of which refute the claim of missing novelty of the study.

Comment 4
"The treatments in statistical analyses are subjective and more explanations or analyses are needed.
For instance, why was the 5 years average selected?What are the differences among the averages of different year windows?Why was the depth of 6 meters applied?Did the authors test other water depth thresholds for the generality of the findings?Why were the additive models selected for TN and TP as I am not well persuaded that these two variables could be simply treated in this way?How were : Christopher T. Filstrup & John A. Downing (2017) Relationship of chlorophyll to phosphorus and nitrogen in nutrient-rich lakes, Inland Waters, 7:4, 385-400, DOI: 10.1080/20442041.2017.1375176Reviewer #2 (Remarks to the Author):

2000 3 ,
the authors find similar thresholds for nine study locations from the open ocean to lakes by using a mix of field and laboratory studies.They have three locations with TN : TP > 50 (Lake Superior, eight other large and small Ontario lakes) and two locations with TN : TP < 20 (Lake Victoria and the Arctic), and use field and laboratory measurements combined with thresholds of phytoplankton N and P growth deficiency based on earlier studies to determine N and P limitation.Therefore, their dataset contains of data from a limited number of locations and makes ecosystem level assumptions based on laboratory measurements of phytoplankton with the notion that such indirect evidence that phytoplankton characteristics might point towards ecosystem N or P deficiency.This is a good start for a search for global stoichiometric deficiency patterns of eutrophication and, indeed, we find similar patterns for 159 lakes based on purely field-based measurements, and across continents, irrespective of climate, land use, lake size, catchment characteristics, with only average lake depth < 6 m as limitation (see also our reply to comment 4 by reviewer 1 for details on that), and based on a rigorous bootstrap resampling to find any uncertainty in our statistical models.Thus, our study provides direct empirical evidence that the N and P deficiency proposed for a few locations in Guildford and Hecky 2000 3 are in fact relevant in lake ecosystems with relevance for shallow lakes which make up more than 80% of all lakes globally.2. A second milestone for our study is Moon et al. 2021 4 .Here, the authors use a US snapshot sampling dataset from more than 1000 lakes with one sample per lake and also find similar patterns as in Guildford and Hecky (2000) 3 , yet with high uncertainty and unclear indication of co-depletion of N and P at intermediate TN : TP ratios.Here, we clearly show the need , the changed figure caption and the changed text linked to figure 4 in the revised manuscrip (lines 128 -131, lines 143 -145) 9. Lines 174-6: Was a regression of nitrate on TN performed?This would give an indication of whether or not nitrate is driving high TN concentrations.Previous work from agricultural regions has shown that nitrate can drive high TN concentrations in lakes (Filstrup and Downing 2017).